1. Technical Field
The embodiments herein generally relate to electrical circuits, and, more particularly, to a digital approach for image rejection correction in low intermediate frequency conversion tuners.
2. Description of the Related Art
A local oscillator (LO) is a device used to generate a signal which is combined with a signal of interest to mix the signal to a different frequency. The LO produces a signal which is injected into the mixer along with the signal from the antenna. This effectively changes the antenna signal by heterodyning with it to produce the sum and difference (e.g., with the utilization of trigonometric angle sum and difference identities) of that signal one of which will be at the intermediate frequency (IF) which can be handled by an IF amplifier. Image rejection (IR) is a measure of a receiver's ability to reject signals at its image frequency. IR is normally expressed as the ratio, in dB, of the receiver's sensitivity at the desired frequency to the sensitivity at the image frequency. A distortion component signal is calculated based on the difference between the current detection signal and the audio signal.
In a low intermediate frequency (LIF) conversion tuner, a desired signal in the radio frequency (RF) is down converted to a LIF signal through the LO, which consists of an in-phase component and a quadrature component. In reality, amplitude and phase of the in-phase component and the quadrature component are usually not balanced. This leads to a leakage of the alternative channel into the desired signal channel band, which is usually referred as image leakage. The image leakage component is a distortion to the desired signal, and its strength depends on the magnitude of the amplitude and the phase imbalance offsets during the LIF down conversion. It is desirable to cancel or remove the image component due to the amplitude and the phase imbalances to improve the received signal quality. The process is usually referred as IR correction.
FIG. 1 is a mathematical flow diagram of a low intermediate frequency down conversion mixer 100. FIG. 1 illustrates how in-phase and quadrature component mismatches are introduced in a quadrature mixer 100, which includes both a phase mismatch and a gain mismatch. For clarity, the gain mismatch (1+α) is put into the in-phase path (cosine), and the phase mismatch (φ) is put into the quadrature path (sine). Within the mixer 100, a received signal x(t) is mixed at nodes 102, 104 with two signals at a predetermined frequency provided from a quadrature generator (not shown). The received RF signal x(t) is mixed with a LO cosine function to generate yr(t) and with the LO sine function to generate yQ(t). A complex IF signal output from the mixer 100 can be expressed as y(t)=yI(t)+i·yQ(t). After some mathematical manipulation, y(t) can be expressed as:
                                                                        y                ⁡                                  (                  t                  )                                            =                            ⁢                                                                    y                    I                                    ⁡                                      (                    t                    )                                                  +                                  ⅈ                  ·                                                            y                      Q                                        ⁡                                          (                      t                      )                                                                                                                                              =                            ⁢                                                [                                                                                    (                                                  1                          +                          α                                                )                                            ⁢                                              cos                        ⁡                                                  (                                                      2                            ⁢                            π                            ⁢                                                                                                                  ⁢                                                          f                              c                                                        ⁢                            t                                                    )                                                                                      -                                          ⅈ                      ·                                              sin                        ⁡                                                  (                                                                                    2                              ⁢                              π                              ⁢                                                                                                                          ⁢                                                              f                                c                                                            ⁢                              t                                                        +                            φ                                                    )                                                                                                      ]                                ·                                  x                  ⁡                                      (                    t                    )                                                                                                                          =                            ⁢                              G                ·                                  (                                                            ⅇ                                                                                                    -                            ⅈ                                                    ·                          2                                                ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          c                                                ⁢                        t                                                              +                                          I                      ·                                              ⅇ                                                                              ⅈ                            ·                            2                                                    ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            c                                                    ⁢                          t                                                                                                      )                                ·                                  x                  ⁡                                      (                    t                    )                                                                                                          (        1        )                                where        ,                                                                      G          =                                    1              2                        ⁢                          (                              1                +                α                +                                  ⅇ                                                            -                      ⅈ                                        ·                    φ                                                              )                                      ,                                  ⁢                  I          =                                                    1                +                α                -                                  ⅇ                                      ⅈ                    ·                    φ                                                                              1                +                α                +                                  ⅇ                                                            -                      ⅈ                                        ·                    φ                                                                        ⁢            0                                              (        2        )            
If α≠0, there will be amplitude imbalance, and it φ≠0, there will be phase imbalance. However in practical analog receivers, there is usually some mismatch, which results in image leakage through the quadrature mixer 100.
FIG. 2 is a graphical diagram 200 showing an IR problem. FIG. 2 illustrates the spectral distribution of an exemplary combination of signals in image leakage. At the input, a desired signal, whose complex baseband representation is S, is present at a frequency fc+fLIF, while an alternative channel, whose complex baseband representation is A, is present at the image frequency of S, fc−fLIF. Signal A represents a signal in a different channel than signal S and has a larger magnitude than signal S. In the illustrated example, signal A is two channels removed from signal S and is referred to as an alternate channel signal relative to signal S. As signals S and A are complex, conjugate signal versions S* and A* exist in the negative frequency plane at frequencies −(fc+fLIF), and −(fc−fLIF), respectively. The amount of image leakage into the desired band is proportional to the magnitude of the interference components I due to the amplitude and phase imbalance offsets.
Traditionally, a combined analog and digital approach is employed to achieve the IR corrections. In these approaches, a training signal is usually required from the analog domain. Interactions between the analog and the digital domain make these types of approaches not very attractive, and the IR performance is also limited to certain degree.